Problem
Use basic identities to $\operatorname{simplify} \sin ^{3} x+\cos ^{2} x \sin x$. Enclose arguments of functions in parentheses. For example, $\sin (2 x)$. Remember that writing $\sin (x)$ to the fourth power as $\sin ^{4}(x)$ is just a mathematical shorthand. You should write it as $(\sin (x))^{4}$, which is what Mobius expects. \[ \sin ^{3} x+\cos ^{2} x \sin x= \]
Solution
Step 1 ：Rewrite the expression as \(\sin^2(x) \sin(x) + \cos^2(x) \sin(x)\)
Step 2 ：Factor out \(\sin(x)\) to get \((\sin^2(x) + \cos^2(x))\sin(x)\)
Step 3 ：Use the Pythagorean identity \(\sin^2(x) + \cos^2(x) = 1\) to simplify
Step 4 ：\(\boxed{\sin(x)}\) is the final answer
